Physiological studies have now reached the point where the parameters of the broadband acoustic stimuli and the statistics of the random process auditory-nerve discharges which represent them may be understood. This suggests that questions concerning the representation of the complex acoustic cues fundamental to discrimination tasks can be resolved. For example, which of the broad array of auditory neurons carries statistically reliable phase-locked frequency information to the cochlear nucleus? Alternatively, how should cells in the central nervous system combine the phase-locked and place coded information across neurons for the frequency discrimination task or for the interaural phase discrimination required for sound localization. The proposed research addresses these questions by developing the Siebert/Gaumond stochastic model an validating it by accounting for the statistics of population responses to simple tone and speech stimuli. From the stochastic model, optimum coding strategies may be developed for the representation of the spectral and phase information fundamental to the discrimination of complex stimuli. The understanding of the coding of these stimuli which this work will provide is essential for the prediction of performance limits for normal as well as hearing impaired, and for the design of cochlear prostheses. This work should also provide a conceptual framework for guiding studies into the complex processing in the central nervous system. For example, optimum processor theory predicts the precise ways in which the information derived from the array of auditory-nerve fibers must converge onto task specific processing cells in higher nuclei so as to maintain the statistical integrity of the frequency and phase information required for the processing task. This work will also provide a new tool for the study of auditory nerve phenomena having to do with onset dynamic range effects, adaptation and the metabolic/physiologic properties of various classes of neurons. The joint maximum-likelihood estimation method for the generation of stimulus and recovery functions will provide a window into the previously unexaminable via spike discharge recordings transduction process between the stimulus related intracellular hair-cell potential and the action potential generation process.